Drawing and sheathing weapons

In short

You can draw or sheathe/stow one weapon or shield per turn as a free action, provided you can take an action.  

In depth

The rules regarding drawing and sheathing weapons are implicit, rather than explicit. PHB page 146 says both equipping and unequipping a shield costs an action. PHB page 190 says that you can interact with one object or feature of the environment for free during either your move or your action. This has been interpreted as drawing or sheathing/stowing a weapon. So you can shoot your bow and stow it on one turn and on the next turn draw and attack with your sword. This essentially means that you cannot swap weapons mid turn. So for simplicity, lets count a shield as a weapon for this matter.  

Edge case: Two weapon thrown fighting

The rules don't seem to explicitly cover two weapon fighting in the context of two thrown weapons. If we follow it implicitly then you can still only draw or sheathe one weapon per turn for free, this would mean you can't keep up two weapon fighting with throwing. You could have two throwing weapons in hand on the first turn, throw both, draw one as part of the free draw in that turn. Second turn you can draw and throw one, throw the one you drew last turn and end the turn with no weapons in hand. Third turn you would have to use an action to draw a weapon, and a free action to draw the other, you still have a bonus action. Now you're back in the situation of the first turn, two weapons in hand. So that is 4 attacks in 3 turns, of which 2 attacks were without damage modifier. To effectively do two weapon thrown fighting you'd need the thrown weapon fighting style. This fighting style allows you to draw as part of the attack (not consuming the free drawing option) and gives a bonus to the damage.